A new derivation of the multigroup transport equations via homogeneity and isotropy restoration theory

This work presents a new consistent derivation of the multigroup transport equations from the original continuous-energy transport equation, achieving group-wise condensation equivalence. The derivation of the multigroup transport equations currently in use involves an important approximation in the total cross section. The homogeneity and isotropy restoration (HIRE) theory described in this paper removes the angle dependency in the group condensed total cross section of the multigroup transport equations. The HIRE theory also restores the homogeneity of each material region, and it frees us from the higher-order moment scattering cross sections. To preserve the reaction rate of the original continuous-energy transport equation, the partial current discontinuity factor (PCDF) is introduced, that is instrumental in the theory. The theory was tested on several pin-cell problems, and the numerical results show that the new multigroup transport equations successfully reproduced the properties of the original continuous-energy transport equation.